Electrical impedance tomography

ABSTRACT

Method and apparatus for obtaining a representation of the distribution of electrical impedance within material contained within a containing wall, comprising providing a plurality of mutually spaced electrodes mounted at spaced locations of the wall, electrically insulated from one another and arranged to be in electrical contact with material contained within the wall, applying between an electrical reference ground and each electrode, separately, an input electrical signal which, while applied to any one of the electrodes, causes respective output electrical signals to be generated between the reference ground and each other one of the electrodes, measuring the output electrical signals and processing the resulting measured data to provide a representation of the distribution, within the said material, of its electrical impedance.

This application claims benefit of international applicationPCT/GB95/00520filed Mar. 10, 1995.

This invention relates to electrical impedance tomography (EIT), whichhas been known for some time in clinical applications and has recentlygained acceptance as a useful technique for rapidly delineating theresistivity distribution of materials inside a process vessel orpipeline.

In the clinical use of EIT, it is known to provide a set of electrodesspaced around, say, the thorax of a patient in electrical contact withthe skin, and to apply a constant current or constant voltage inputelectrical signal between each in turn of all the possible mutuallyadjacent pairs of electrodes. While the input signal is being applied toany one pair of mutually adjacent electrodes, the currents or voltagesbetween each mutually adjacent pair of the remainder of the electrodesare measured and the resulting measured-data are processed in knownmanner to yield, and display on a screen, a representation of thedistribution of the electrical resistivity across a cross section of thepatient which is bounded by the ring of electrodes.

It is also known from U.S. Pat. 5,272,624 to employ a medical electricalimpedance imaging technique using set current patterns, in whichelectrical current is simultaneously injected to each of an array ofspaced electrodes around the periphery of the body under investigation,the amplitude of the current varying according to, say, a cosinusoidaldistribution around the periphery. The pattern of injected current isthen successively altered around the electrode array, and the amplitudeof the input signal is adapted to give the optimum distinguishabilityfor the particular application of interest.

The technique of U.S. Pat. No. 5,272,624 involves the measurement of thevoltages developed at or near each electrode with respect to a commonpoint, or earth reference. However, the currents are injectedindependently of this earth reference.

It has also become known to apply EIT to vessels and pipelines made ofelectrically non-conductive material, such as acrylic or other plasticsmaterials, in order to determine the resistivity distribution, over across-section of the vessel or pipeline, of its contents, notably whenthese are or may be a suspension of solids in a liquid of differentresistivity, or a plurality of mutually immiscible liquids of differentresistivities. In this application of EIT, it is known to provide thatthe electrodes are mounted in and project through the vessel or pipelinewall so as to be directly in electrical contact with the contentswithin. Only a minor modification of the data processing algorithm isrequired to take account of the fact that the pairs of electrodesbetween which an input signal is applied or an output signal is measuredmay now be actually or effectively within (though usually only slightlywithin) the body of material of which the resistivity distribution is tobe determined.

It has also been proposed to employ EIT in connection with vessels andpipelines made of electrically conductive materials. Clearly, since mostindustrial pipelines and process vessels are constructed fromelectrically conductive metallic materials, there is a practical need tomodify existing EIT techniques as may be necessary to accommodate suchmaterials. Since it is necessary to keep the electrodes insulated fromone another, it is necessary to insulate them from the conductivecontaining wall and to arrange that they project through the wall intodirect electrical contact with the contents within. Even when that isdone, however, it is found that, when an input signal is applied betweenone pair of adjacent electrodes, output signals measured between otherpairs of mutually adjacent electrodes are of low amplitude andconsequently have a poor signal-to-noise ratio leading, after signalprocessing in known manner, to a resistivity-distribution determinationof unsatisfactorily poor quality.

A useful summary of the applications of EIT to fluid mixtures in processreactors and pipelines can be found in "Determination of Composition andMotion of Multicomponent Mixtures in Process Vessels using ElectricalImpedance Tomography-I. Principles and Process Engineering Applications"F. J. Dickin et al, Chemical Engineering Science, Vol. 48, No. 10, 1993,pp. 1883-1897.

SUMMARY OF THE INVENTION

It is an object of the present invention to provide an EIT method andapparatus which may be successfully employed in conjunction with acontaining wall of either electrically non-conductive or electricallyconductive material.

According to a first aspect of the invention there is provided a methodof obtaining a representation of the distribution of electricalimpedance within material contained within a containing wall, comprisingproviding a plurality of mutually spaced electrodes mounted at spacedlocations of the wall, electrically insulated from one another andarranged to be in electrical contact with material contained within thewall, applying between an electrical reference ground and eachelectrode, separately, an input electrical signal which, while appliedto any one of the electrodes, causes respective output electricalsignals to be generated between the reference ground and each other oneof the electrodes, measuring the output electrical signals andprocessing the resulting measured data to provide a representation ofthe distribution, within the said material, of its electrical impedance.

According to another aspect of the invention there is provided apparatusfor obtaining a representation of the distribution of electricalimpedance within a body of material, comprising container means having acontaining wall for containing the material, a plurality of electrodesmounted at spaced locations of the wall, electrically insulated from oneanother and arranged to be in electrical contact with material containedwithin the wall, means for generating, and applying between anelectrical reference ground and each electrode, separately, an inputsignal which, while applied to any one of the electrodes, causesrespective output electrical signals to be generated between thereference ground and each other one of the electrodes, means formeasuring the output electrical signals, and means for processing theresulting measured data and providing a representation of thedistribution, within the said material, of its electrical impedance.

In applying the method and apparatus according to the invention in acase where the containing wall is of electrically conductive material,the wall itself is preferably made to serve as the reference groundrelative to which the input and output electrical signals are appliedand measured, preferably with the electrodes mounted in the wall butelectrically insulated from it, and protruding through it into contactwith the material contained within it.

If the containing wall is non-conductive, other means of providing thereference ground must be devised. To that end, it may be arranged thatthe reference ground is constituted, at any given moment, by all theelectrodes, electrically strapped together, except for one of theelectrodes to which an input signal is being applied relative to thereference ground, and one other of the electrodes at which an outputelectrical signal is being measured relative to the reference ground.

In another embodiment of the invention, the reference ground is providedby at least one electrode positioned within, and away from the boundaryof, the material whose impedance distribution is to be reconstructed.This reference ground electrode may or may not be positioned at thecentre of the vessel. If an electrically conductive component of theapparatus, such as a stirrer, is positioned within the vessel it may bemade to serve as the reference ground electrode.

In a modification, in clinical use of the invention, the patient's skinconstitutes the boundary of the material whose impedance distribution isto be reconstructed, and no other containing wall requires to beprovided. In such a case, the electrodes are applied to the skin inknown manner and are not required to protrude through it.

BREIF DESCRIPTION OF THE DRAWINGS

The invention will be further explained and elucidated in the followingdescription referring to both method and apparatus, with reference tothe accompanying drawings, in which:

FIG. 1 represents a known kind of EIT applied to material contained in acircular-section vessel or pipeline of which the containing wall is ofelectrically non- conductive material;

FIG. 2 represents an application of EIT in accordance with the inventionto material contained in a circular-section vessel or pipeline of whichthe containing wall is of electrically conductive material such as ametal;

FIG. 3 is a schematic sectional view of one of a plurality of similarelectrodes mounted in the electrically conductive containing wall shownin FIG. 2 but electrically insulated from the wall and from each other;

FIG. 4 represents the electrical potentials which, when a givenelectrical potential or current is applied to one of the electrodesshown in FIG. 2, may be measured at the other such electrodes;

FIG. 5 is a representation of pixel sensitivity coefficients as used inimplementing an image reconstruction in accordance with the invention;

FIG. 6 is a reconstructed image of three glass rods dipping into watercontained in a metal-walled vessel;

FIG. 7 represents an electrically non-conductive vessel wall fitted witha plurality of electrodes and illustrates a suitable arrangement ofelectrode connections for use in carrying out the invention; and

FIG. 8, similar to FIG. 7, illustrates another suitable arrangement ofelectrode connections for use in carrying out the invention.

DETAILED DESCRIPTION OF THE PRESENTLY PRREFERRED EXEMPLARY EMBODIMENT

In the known application of EIT illustrated in FIG. 1, material 20 ofwhich the resistivity distribution is to be determined is contained in apipeline or other vessel having a circular wall 21 of acrylic or otherelectrically insulating material, and a plurality of electrodes 22 aremounted in the wall 21, equally spaced around it and each projectingthrough the wall so as to be in contact, inside the wall, with thematerial 20 and accessible, outside the wall, for attachment of anelectrical connection. As shown diagrammatically in FIG. 1, a source 23of constant current is connected between one mutually adjacent pair ofthe electrodes 22, and a voltage measuring device 24 is connectedbetween a mutually adjacent pair of the remaining electrodes 22 tomeasure the voltage existing between those electrodes in consequence ofthe current flowing between the pair of electrodes to which the source23 is connected. In performing this form of EIT, the current source 23would be maintained connected between the one pair of mutually adjacentelectrodes while the voltages between each other mutually adjacent pairof the remaining electrodes is similarly measured. The current source 23would then be connected between a different pair of mutually adjacentelectrodes, while the resulting voltages between each mutually adjacentpair of the then remaining electrodes was measured, and the processwould be repeated until the current source had been applied between eachpair of mutually adjacent electrodes and, for each pair, thecorresponding voltages between each mutually adjacent pair of theremaining electrodes had been measured. All the measured data would thenbe processed, in known manner, by computer means (not shown) to yield arepresentation of the distribution of electrical resistivity in thematerial 20.

FIG. 1 also shows, for the case where the material 20 is of uniformelectrical resistivity, the system of equipotential lines 25 and currentstreamlines 26 which characiterize the electrical field which isproduced in the material 20 by applying an input electrical signal fromthe source 23 between one pair of mutually adjacent electrodes 22. Itwill be seen that the equipotential lines 25 fan out in such a way thatelements of the wall 21 at different positions round its periphery areall at different potentials, and this would remain true even if thematerial 20 were not of uniform resistivity and there were inconsequence a greater or lesser degree of perturbation of the symmetryand regularity of the illustrated pattern of equipotential lines andcurrent streamlines. It will be clear that the type of field patternillustrated in FIG. I cannot obtain if the electrically insulating wall20 is replaced by an electrically conductive wall, since, the greaterits conductivity, the more closely will it approximate to anequipotential surface.

As already noted above, if the containing wall is conductive it isnecessary to insulate the electrodes from it. Even if that is done,however, an input signal applied by the source 23 between two adjacentelectrodes, as shown in FIG. 1, would be to a large extent shortcircuited by the part of the conductive wall extending between the twoelectrodes. An output signal measured between two other mutuallyadjacent ones of the electrodes would be of unacceptably low amplitudeboth because the field generated in the material 20 at a distance fromthe electrodes between which the source 23 is connected would be reducedby the short-circuiting effect of the wall between those electrodes andalso because of a similar short-circuiting effect due to the presence ofthe conductive wall extending between the pair of electrodes betweenwhich the output signal was being measured.

In practicing the present invention, however, the input and outputelectrical signals are applied or measured not between pairs ofelectrodes but, in each case, between an individual electrode and acommon electrical reference ground. In the embodiment of the inventionillustrated diagrammatically in FIG. 2, in which an electricallyconductive containing wall is referenced 21A to distinguish it from theinsulating wall 21 of FIG. 1, this conductive containing wall serves asthe common electrical reference point, or ground.

Each of the electrodes 22 mounted in the wall 21A, and numbered 1-16,respectively, is electrically insulated from the wall, for example bymeans of an insulating sleeve 27, as shown in FIG. 3. It may beremarked, however, that the mounting of the electrodes in the wall 21Amay in practice need to be more complicated than shown in FIG. 3, sincethe material 20 within the wall 21A may be under substantial pressurewhich the electrodes and their mountings must be capable of resisting.

In accordance with the invention, and as shown in FIG. 2, an inputelectrical signal provided by the source 23 is applied between ground,i.e. the conductive wall 21A, and a single one of the electrodes 22(that numbered 16, as illustrated) while output electrical signals aremeasured between each of the remaining electrodes 22 (numbered 1-15respectively) and ground, by measuring means 24 as shown connectedbetween ground and the electrode 22 numbered 10. Corresponding sets ofoutput signals are measured while an input signal is applied to eachother of the electrodes 22 individually, and the totality of measureddata is then processed by the use of an appropriate algorithm to derivea representation of the resistivity distribution within the material 20.FIG. 2 also shows, for the case of uniform resistivity of the material20, the equipotential lines 25 and current streamlines 26 of the fieldpattern established in the material 20 by applying an input signal fromthe source 23 between ground (the wall 21 A) and the electrode 22 whichis numbered 16. It will be observed that the field pattern obtained inthis case is quite different from that shown in FIG. 1: in fact, theequipotential lines and current streamlines (which are always mutuallyorthogonal) have virtually interchanged with one another as betweenFIGS. 1 and 2. If, as indicated in FIG. 2, the input signal is aninjected current (for example of 1.5 mA per cm peak-to-peak at afrequency of 9.6 kHz) applied to one electrode 22 and the output signalsare the potentials of the other electrodes 22 relative to the wall 21A(from which, of course, they are insulated) those electrodes which areremote from that one to which the input signal is applied from thesource 23 are relatively unaffected by the input signal, while theeffect is progressively greater on those electrodes which are closer.This is illustrated by FIG. 4, which shows typical voltages measured (inmillivolts) at each of the electrodes numbered 1-15 when the inputsignal is applied to the electrode numbered 16, as shown in FIG. 2. Thevoltage output signals thus obtained are substantially greater thanwould be measured between pairs of adjacent electrodes, with the sameinput signal applied between one such pair (as described with referenceto FIG. 1) but subject to the grounding or short-circuiting effect whichis produced by an electrically conductive wall even though theelectrodes are insulated from it.

The presence of the insulators 27, and the corresponding absence thereof conductive material continuous with that of the wall 21A and atground potential, has a slight distorting effect on the field pattern inthe material 20 immediately adjacent the electrodes. It may be shownthat this effect results in the potential measured at an electrode beingsimilar to that which would be measured by an electrode positioned adistance s/4 inside the wall if the wall presented a continuous surfaceat ground potential, where s is the external diameter of the insulator27. That is, if the actual radius of the wall 21A is R_(o), the radiusof the circle on which the electrodes are disposed is effectively R_(e)where R_(e) =R_(o) -s/4. An "intrusive effect", g, of the presence ofthe insulators of diameter s can then be defined as g =R_(o/R) _(e).Since s<<R_(o), the distortion of the electric field produced in thematerial 20 by applying a current to one of the electrodes 22 isgreatest in the vicinity of the wall 21A but rapidly becomes negligibleat smaller radii.

It may be shown that, for a material 20 of uniform conductivity σ,injection at one electrode 22 of a current IL produces, at an electrodespaced round the wall 21A by an angle (π-θ), a voltage V(R_(e),θ) givenby ##EQU1##

This is the distribution of induced voltage on the electrodes which isillustrated in FIG. 4. The similarity between this voltage profile andthat obtained in the case of an insulating vessel wall, by applying aninput current signal between a pair of adjacent electrodes as describedabove with reference to FIG. 1, provided an early confirmation that thepresent invention may be practiced using data acquisition systems(source 23 and output signal measuring means 24) already available foruse with a non-conductive vessel wall, with at most only minormodifications to the current injection and voltage buffer circuitrybeing required.

In the case of non-uniformity of the conductivity of the material 20,essentially the same image reconstruction algorithms may be employedwhen the container wall is of electrically conductive material as arealready known and in use in connection with EIT of material containedwithin a non-conductive pipeline or other vessel. For example, inpracticing the invention in conjunction with an electrically conductivecontainer wall, as described above with reference to FIG. 2, use hasbeen made of a qualitative image reconstruction algorithm employing thesensitivity coefficient method described by C. J. Kotre in Clin. Phys.Physiol. Meas., 1989, 10(3), 275-281. FIG. 5 shows the sensitivitycoefficients of the pixels for the case where the electrodes to which aninput signal is applied and at which an output signal is measured arediametrically opposite to one another, as for example the electrodesnumbered 16 and 8 in FIG. 3.

It can be seen that there is a high sensitivity in the regions close toboth electrodes but that the sensitivity decreases rapidly away fromthose regions. By utilizing a sequence of sensitivity maps,corresponding to all the possible drive/measure combinations, aqualitative image is reconstructed showing the variations inconductivity across the cross-section of the material 20 within thevessel 21A at the level of the electrodes 22. FIG. 6 shows areconstructed image, obtained in this way, of three 1-cm diameter glassrods spaced approximately 2 cm from the boundary of the vessel 21A of16.6 cm diameter which was filled with tap water. The regions of lightershade in FIG. 6 represent areas of relatively low conductivity andcorrespond to the positions of the three glass rods, and the darkerparts of the image correspond to the surrounding water.

The sensitivity theorem for an electrically conducting body, asoriginally developed by Geselowitz and later refined by Lehr, in essenceenabled the impedance properties of a body to be determined from a4-electrode (two-port) current excitation/ voltage measurement techniqueas illustrated in FIG. 1. However, the theorem was developed on thebasis that the outer layer of the body was electrically non-conducting.For the purpose of the present invention, the original four-leadtwo-port model is modified into an equivalent three-lead two-port modelwith, in the example shown in FIG. 2, the conducting boundary wall 21Aserving as the third lead. Despite this modification, theGeselowitz/Lehr theorem is unchanged and the discretized arearepresenting a two-dimensional cross-section of the vessel can betreated with Geselowitz's method to determine the sensitivitycoefficient of each of the discretized regions. In the image shown inFIG. 6 the circular cross-section of the vessel was divided into a setof 7,680 square pixels having a radius of 100 square pixels. Thesensitivity coefficient S for each of these pixels was calculated usingthe Geselowitz method, and the reconstructed image composed of pixelgrey-levels P_(x),y was formed, as proposed by Kotre, from the productof these coefficients with the logarithm of the ratio of measuredvoltages.

It will be understood that although the image shown in FIG. 6 wasobtained by use of an image reconstruction algorithm employing the Kotresensitivity coefficient method, other known methods of processing themeasured data to obtain the desired image may also be employed. Forexample, a finite element method (FEM), appropriately matched to thechanged boundary conditions, may equally well be employed.

It will be understood that although the foregoing specification refersto resistance and resistivity of the material under investigation, EITgenerally and the present invention in particular may be used forinvestigating impedance generally and not only its resistive component;and that accordingly the references to resistance and resistivity are tobe understood in the wider sense of impedance.

It will be understood also that, although the invention is particularlyadapted for use in overcoming the difficulties encountered in applyingEIT in conjunction with a container wall of electrically conductivematerial, it may with advantage also be applied in the case of vesselshaving electrically non-conductive walls or, indeed, in clinical usewhere the boundary of the sample is the patient's skin which is of highimpedance in directions along the surface. In such cases, of course, itis not possible to use the (non-conductive) container wall as the commonelectrical reference ground, but other arrangements may be made, forexample as will now be described with reference to FIGS. 7 and 8.

As shown in FIG. 7, material 20, of whose impedance distribution animage is to be reconstructed, is contained within a pipeline or othervessel having an electrically non-conductive wall 21 in which aremounted, protruding through the wall into electrical contact with thematerial 20, a plurality of electrodes 22 numbered I to 16. Alsoprovided are a source 23 for applying input electrical signals toselected electrodes 22 and an output signal measuring device 24 formeasuring output signals from selected electrodes 22. Thus far, thearrangement is as described with reference to FIG. 1 of theaforementioned co-pending application. As shown in FIG. 7, however, eachelectrode 22 is connected to a respective 3-way switch 28 by which itcan be connected to a common connector strap 29 to serve as part of areference ground of the system, or to a connection 30 or to a connection31. The signal source 23 is connected to apply input signals between thereference ground strap 29 and the connection 30 and any electrode 22connected thereto, and the signal measuring means 24 is similarlyconnected to measure output signals generated between the strap 29 andthe connection 31 and any electrode connected thereto. In use of thissystem, at any given moment during data collection all the electrodes 22are connected by their respective switches 28 to the strap 29 to form areference ground of the system, except for one electrode 22 (thatnumbered I as shown in FIG. 7) which is switched to receive an inputsignal applied by the source 23 between it and the reference ground, andone (that numbered 10 as shown in FIG. 7) which is connected to theconnection 31 to provide an output signal to the device 24. Each of theelectrodes 22 is connected, separately, to the connection 29 forapplication to it of an input signal during an interval during whicheach other electrode, separately, is connected to the connection 31 formeasurement of an output signal by the device 24. Thus at any time allexcept two of the electrodes combine to provide the system referenceground.

The arrangement shown in FIG. 8 is generally similar to that describedabove with reference to FIG. 7, but is provided, within the vesselcontaining the material 20, with a stirrer having an electricallyconductive shaft 32 with paddle blades 33 which may be non-conductive.In this case the stirrer shaft 32 serves as the reference ground and thesignal source 23 and measuring device 24 are connected between thestirrer and, respectively, the connections 30 and 31. The strap 29 shownin FIG. 7 may be omitted as shown, and any electrode 22 which is notconnected by its switch 28 to the connection 30 or 31 is then leftdisconnected and floating. It will be understood that the algorithmsused in processing the measured data obtained as described withreference to FIGS. 7 and 8, or in further variants described below, willusually require appropriate, modification to take account of theparticular boundary conditions set up by the electrode connections. Useof a reference ground electrode at or near the centre of the vessel asshown in FIG. 8 is effective to increase the sensitivity of the systemnear the centre of the vessel where, otherwise, it is low compared withthe sensitivity near the peripheral boundary.

If a stirrer or other electrode as shown in FIG. 8 is provided withinthe material 20 in an arrangement which is otherwise as shown in FIG. 7,it may also be provided, like each peripheral electrode 22, with switchmeans to connect it either to the reference ground connection 29 or viathe connections 30 and 31 to either the input signal source 23 or theoutput signal measuring means 24. This enables an input signal to beapplied to it while an output signal is measured at each of theelectrodes 22, one after another, and also enables successive outputsignals to be measured at the inner electrode as input signals areapplied to each of the electrodes 22, one after another. By this meansadditional measurement data can be acquired which improves thesensitivity of the system in respect of parts of the material 20 whichare remote from the wall 21.

It may be mentioned here that, analogous with FIG. 8, or with theabove-described modification of FIG. 7 to provide it with an innerelectrode at which an input signal may be applied or an output signalmay be measured, or which may serve as the, or part of the, signalreference ground, such an inner electrode may similarly be employed whensingle-electrode excitation and measurement in accordance with theinvention are employed in clinical practice. Thus in EIT thoracicexaminations in accordance with the invention, an inner electrode at thefree end of an insulated cable may be passed down the oesophagus to therequired level within the thorax (as has indeed already been proposed inthe case of conventional EIT using two-electrode signal input andtwo-electrode output signal measurement).

As illustrated by FIGS. I and 2, the provision of an electricallyconductive boundary round the body of material which is to beinvestigated has the effect of interchanging the pattern ofequipotential lines and current streamlines in the body, as comparedwith the case where the boundary is non-conductive. There may becircumstances in which advantage can be taken of this fact in theclinical use of EIT. For example, the electrodes to be applied to apatient may be mounted in insulated manner in a band or belt ofelectrically conductive (and preferably elastic) material which can thenbe fitted round the part of the patient which is to be investigated. Orthe belt may be of non-conductive material, but fitted with compoundelectrodes such as those suggested in a paper: "Using CompoundElectrodes in EIT" (Ping Hua et al, IEEE Trans. in Biomed. Eng., 40, No.1 (Jan 1993)). As there proposed, a compound electrode comprises a smallinner electrode surrounded by an outer electrode of much larger surfacearea, the intention being that an input current signal can be appliedbetween the outer electrodes of two compound electrodes while an outputvoltage signal is measured between the inner electrodes of the same or adifferent pair of compound electrodes. A belt of such compoundelectrodes may also, however, be used in carrying out EIT in accordancewith the present invention if it is fitted to a patient and all itsouter electrodes are strapped together as an effective conductive outerboundary and as a signal reference ground, while input and outputsignals, relative to the reference ground, are applied to or measured atindividual inner electrodes of the compound electrodes.

We claim:
 1. A method of obtaining a representation of the distributionof electrical impedance within material contained within a containingwall, the method comprising:providing a plurality of mutually spacedelectrodes mounted at spaced locations of the wall, the electrodes beingelectrically insulated from one another and arranged to be in electricalcontact with material contained within the wall; applying, between anelectrical reference ground and each electrode, sequentially, an inputelectrical signal which, while applied to any one of the electrodes,causes respective output electrical signals to be generated between theelectrical reference ground and each other one of the electrodes;measuring said output electrical signals generated between theelectrical reference ground and each other one of the electrodes; andprocessing the resulting measured data to provide a representation ofthe distribution, within said material, of its electrical impedance. 2.A method as claimed in claim 1 wherein the containing wall iselectrically conductive and is employed as said electrical referenceground relative to which the input and output electrical signals areapplied and measured.
 3. A method as claimed in claim 1 wherein thecontaining wall is electrically non-conductive, and wherein saidelectrical reference ground is formed by connecting together, at any onetime, all the electrodes except those two electrodes at which,respectively, an input signal is being applied and an output signal isbeing measured.
 4. A method as claimed in claim 1 further comprisingproviding, as said electrical reference ground, an electrode within, andspaced from the boundary of, said material.
 5. A method as claimed inclaim 1, in clinical uses wherein said containing wall comprises theskin of a patient and wherein the electrodes are applied in contact withthe skin.
 6. A method as claimed in claim 5, wherein the electrodes arefitted to a belt and the belt is fitted around a part of the patient. 7.A method as claimed in claim 6, wherein the belt is electricallyconductive and electrically insulated from the electrode and is employedas said electrical reference ground.
 8. Apparatus for obtaining arepresentation of the distribution of electrical impedance within a bodyof material, the apparatus comprising:a container having a containingwall for containing the material; a plurality of electrodes mounted atspaced locations of the wall, electrically insulated from one anotherand arranged to be in electrical contact with material contained withinthe wall; means for generating, and for applying between an electricalreference ground and each electrode, sequentially, an input signalwhich, while applied to any one of the electrodes, causes respectiveoutput electrical signals to be generated between the electricalreference ground and each other one of the electrodes; means formeasuring the output electrical signals generated between the electricalreference ground and each other one of the electrodes; and means forprocessing the resulting measured data and providing a representation ofthe distribution, within said material, of its electrical impedance. 9.Apparatus as claimed in claim 8, wherein said electrodes are mounted inthe wall and protrude therethrough to be in electrical contact with thematerial contained within the wall.
 10. Apparatus as claimed in claim 9,wherein said containing wall is electrically conductive and theelectrodes mounted in it are electrically insulated from it. 11.Apparatus as claimed in claim 8, wherein the containing wall iselectrically conductive and constitutes said electrical reference groundrelative to which the input and output electrical signals are appliedand measured.
 12. Apparatus as claimed in claim 8 wherein the containingwall is electrically nonconductive and, for constituting said electricalreference ground, there are provided switch means for connectingtogether, at any one time, all the electrodes except those twoelectrodes at which, respectively, an input signal is being applied andan output signal is being measured.
 13. Apparatus as claimed in claim 8,and including, as the electrical reference ground, an electrode within,and spaced from the boundary of, said material.
 14. Apparatus as claimedin claim 13, wherein the electrical reference ground is constituted bymeans, such as a stirrer, which also serves another purpose. 15.Apparatus as claimed in claim 8, in clinical use, wherein the electrodesare arranged for contact with a patient's skin.
 16. Apparatus as claimedin claim 15, wherein the electrodes are fitted to a belt and the belt isfitted around a part of the patient.
 17. Apparatus as claimed in claim16, wherein the belt is electrically conductive and electricallyinsulated from the electrodes and constitutes said electrical referenceground.